\[ \int \frac {x^5}{\left (b x^2+c x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \left (\frac {x^{2} \sqrt {c}}{\sqrt {c \,x^{4}+b \,x^{2}}}\right )}{c^{\frac {3}{2}}}-\frac {x^{2}}{c \sqrt {c \,x^{4}+b \,x^{2}}} \]
command
integrate(x^5/(c*x^4+b*x^2)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\log \left ({\left | b \right |}\right ) \mathrm {sgn}\left (x\right )}{2 \, c^{\frac {3}{2}}} - \frac {x}{\sqrt {c x^{2} + b} c \mathrm {sgn}\left (x\right )} - \frac {\log \left ({\left | -\sqrt {c} x + \sqrt {c x^{2} + b} \right |}\right )}{c^{\frac {3}{2}} \mathrm {sgn}\left (x\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________